Problem: Given $ m \angle LOM = 5x + 54$, and $ m \angle MON = 6x + 104$, find $m\angle MON$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {5x + 54} + {6x + 104} = {180}$ Combine like terms: $ 11x + 158 = 180$ Subtract $158$ from both sides: $ 11x = 22$ Divide both sides by $11$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 6({2}) + 104$ Simplify: $ {m\angle MON = 12 + 104}$ So ${m\angle MON = 116}$.